Probabilistic seismic hazard analysis has been used extensively for major dams; nuclear power plants; liquefied petroleum gas installations; repositories for dangerous wastes; sensitive industrial, business and defense installations; fire stations; schools and hospitals. However, a large body of evidence shows seismic probability theory to be defective for estimating earthquakes greater than magnitude 5.0. It is time to reexamine the current, almost total, acceptance of seismic probability for the engineering of critical structures.